English
Related papers

Related papers: Pendant appearances and components in random graph…

200 papers

The poster presents an analytic formalism describing metric properties of undirected random graphs with arbitrary degree distributions and statistically uncorrelated (i.e. randomly connected) vertices. The formalism allows to calculate the…

Statistical Mechanics · Physics 2007-05-23 Agata Fronczak , Piotr Fronczak , Janusz A. Holyst

We investigate the dynamic formation of regular random graphs. In our model, we pick a pair of nodes at random and connect them with a link if both of their degrees are smaller than d. Starting with a set of isolated nodes, we repeat this…

Statistical Mechanics · Physics 2011-11-16 E. Ben-Naim , P. L. Krapivsky

We investigate the distribution of eigenvalues of weighted adjacency matrices from a specific ensemble of random graphs. We distribute $N$ vertices across a fixed number $\kappa$ of components, with asymptotically $\alpha_j \dot N$ vertices…

Mathematical Physics · Physics 2024-09-30 Valentin Vengerovsky

We find an asymptotic enumeration formula for the number of simple $r$-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations.…

Combinatorics · Mathematics 2022-05-18 Catherine Greenhill , Mikhail Isaev , Tamás Makai , Brendan D. McKay

We consider 15 properties of labeled random graphs that are of interest in the graph-theoretical and the graph mining literature, such as clustering coefficients, centrality measures, spectral radius, degree assortativity, treedepth,…

Social and Information Networks · Computer Science 2022-06-24 Hang Chen , Vahan Huroyan , Stephen Kobourov , Myroslav Kryven

Paper proposes a model of large networks based on a random preferential attachment graph with addition of complete subgraphs (cliques). The proposed model refers to models of random graphs following the nonlinear preferential attachment…

Social and Information Networks · Computer Science 2019-04-05 E. B. Yudin

The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…

Probability · Mathematics 2017-04-19 Richard Kenyon , Mei Yin

One of the main questions that arise when studying random and quasi-random structures is which properties P are such that any object that satisfies P "behaves" like a truly random one. In the context of graphs, Chung, Graham, and Wilson…

Combinatorics · Mathematics 2009-03-03 Asaf Shapira , Raphael Yuster

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…

Statistical Mechanics · Physics 2025-07-01 Dario Borrelli

Given a graphical degree sequence ${\bf d}=(d_1,\ldots, d_n)$, let $G(n, {\bf d})$ denote a uniformly random graph on vertex set $[n]$ where vertex $ i$ has degree $d_i$ for every $1\le i\le n$. We give upper and lower bounds on the joint…

Combinatorics · Mathematics 2025-05-28 Pu Gao , Yuval Ohapkin

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

Combinatorics · Mathematics 2025-06-30 Sean Mandrick

We consider a Laplace operator on a random graph consisting of infinitely many loops joined symmetrically by intervals of unit length. The arc lengths of the loops are considered to be independent, identically distributed random variables.…

Mathematical Physics · Physics 2007-05-23 Vadim Kostrykin , Robert Schrader

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…

Probability · Mathematics 2022-05-04 Omer Bobrowski , Dmitri Krioukov

Consider the geometric graph on $n$ independent uniform random points in a connected compact region $A$ of ${\bf R}^d, d \geq 2$, with $C^2$ boundary, or in the unit square, with distance parameter $r_n$. Let $K_n$ be the number of…

Probability · Mathematics 2026-04-09 Mathew D. Penrose , Xiaochuan Yang

The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and opens avenues for new constructions of knots and other topological objects with interesting properties. The knotting of…

Geometric Topology · Mathematics 2018-04-27 Chaim Even-Zohar

We consider a class of growing random graphs obtained by creating vertices sequentially one by one: at each step, we choose uniformly the neighbours of the newly created vertex; its degree is a random variable with a fixed but arbitrary…

Combinatorics · Mathematics 2013-11-13 Svante Janson , Simone Severini

We study the evolution of graphs densifying by adding edges: Two vertices are chosen randomly, and an edge is (i) established if each vertex belongs to a tree; (ii) established with probability $p$ if only one vertex belongs to a tree;…

Probability · Mathematics 2024-09-10 P. L. Krapivsky

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

Statistical Mechanics · Physics 2009-11-07 Stephane Coulomb , Michel Bauer

In a random graph, counts for the number of vertices with given degrees will typically be dependent. We show via a multivariate normal and a Poisson process approximation that, for graphs which have independent edges, with a possibly…

Probability · Mathematics 2009-12-25 K. Lin , G. Reinert

We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…

Computational Geometry · Computer Science 2007-05-23 David Eppstein , Michael T. Goodrich , Jeremy Yu Meng